3384 HYDROGRAPHIC MANUAL PaGE 240 



noon line of position. Further adjustments may be required when the intermediate 

 lines of position are considered. In some circumstances the procedure should be 

 reversed and the position of the line made to agree with the noon sight first, the log 

 factor being determined afterward. The above example is oversimplified because 

 sounding lines are rarely run exactly east or west and morning and afternoon sun sights 

 are rarely obtained when the sun is exactly on the prime vertical. It will serve, how- 

 ever, to explain the method which, of course, has to be modified to meet each individual 

 case. 



Where the direction of the line is such that it is neither parallel nor perpendicular 

 to lines of position which can be used as described above, the preliminary log factor to 

 be used during the day must be determined from the interval between the fixes obtained 

 at morning and evening star sights. Otherwise the line must be adjusted by a trial- 

 and-error method, trying various log factors and positions of the line until its most 

 probable relation to the lines of position has been determined. 



3384. Accuracy of Astronomic Observations 



Astronomic observations should be made with navigating sextants, read to the 

 nearest 10 seconds, and the time of each observation marked to the nearest fifth of a 

 second. ' When only one person is observing at a time, the times of the observations 

 may be marked by the recorder on the chronometer, if it is conveniently located. 

 "WTien two or more observers are engaged simultaneously in taking star sights, it is 

 impracticable to use the chronometer for all observations. In such cases and when the 

 chronometer is not accessible, best results are obtained by the use of a stop watch 

 which should be compared with the chronometer immediately before and after a series 

 of observations. For stellar observations each observer should have his own recorder 

 and stop watch. 



In astronomic observations a change of 1 minute in altitude moves the line of 

 position 1 nautical mile, a fact which should always be borne in mind. An observa- 

 tional error of 15 seconds in altitude will make an error of one-fourth nautical mile in 

 the line of position. 



At the Equator the altitude of a celestial body on the prime vertical changes 1 

 minute of arc in 4 seconds of time. Therefore, if the time of observation is 1 second 

 in error, the resulting line of position will be in error one-fourth of a nautical mile. 

 For other latitudes and other azimuths the error in position caused by an error in time 

 is correspondingly less, varying with the cosine of the latitude and the sine of the 

 azimuth measured from the pole. This is represented by the following formula: 



Position error (in nautical miles) =7 cos </> sin a 



in which t is the time in seconds, </> is the latitude of the observer, and a is the azimuth 

 of the observed body east or west of the elevated pole of the observer. 



It is probable that a careful observation on one star, made under the best conditions 

 with an accurate sextant in good adjustment, can be counted on to give a line of position 

 correct within one-half mile. And, in general, the accuracy of an individual sun sight 

 observed under similarly good conditions is somewhat greater. 



A series of star sights which was analyzed in 1930 had an average intercept of 0.93 

 nautical mile. These sights were made by several observers; unreliable sights were 

 rejected from the average; the sights were observed from a vessel at anchor; but some 

 of the other conditions were not the best. The results showed practically no personal 

 error. 



